Results 1 to 10 of about 85,369,012 (181)

On numerical simulation of liquid polymer moulding

Mathematical Modelling and Analysis, 2003
In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
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Causality-Aware Training of Physics-Informed Neural Networks for Solving Inverse Problems

Mathematics
Inverse Physics-Informed Neural Networks (inverse PINNs) offer a robust framework for solving inverse problems governed by partial differential equations (PDEs), particularly in scenarios with limited or noisy data. However, conventional inverse PINNs do
Jaeseung Kim, Hwijae Son
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Gradient Statistics-Based Multi-Objective Optimization in Physics-Informed Neural Networks

Sensors, 2023
Modeling and simulation of complex non-linear systems are essential in physics, engineering, and signal processing. Neural networks are widely regarded for such tasks due to their ability to learn complex representations from data.
Sai Karthikeya Vemuri, Joachim Denzler
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Families of Orbits Produced by Three-Dimensional Central and Polynomial Potentials: An Application to the 3D Harmonic Oscillator

Axioms, 2023
We study three-dimensional potentials of the form V=U(xp+yp+zp), where U is an arbitrary function of C2-class, and p∈Z, which produces a preassigned two-parametric family of spatial regular orbits given in the solved form f(x,y,z) = c1, g(x,y,z) = c2 (c1,
Thomas Kotoulas
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Physics-informed linear model (PILM): analytical representations and application to crustal strain rate estimation

Earth, Planets and Space
Many physical systems are described by partial differential equations (PDEs), and solving these equations and estimating their coefficients or boundary conditions (BCs) from observational data play a crucial role in understanding the associated phenomena.
Tomohisa Okazaki
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Collage-type approach to inverse problems for elliptic PDEs on perforated domains

Electronic Journal of Differential Equations, 2015
We present a collage-based method for solving inverse problems for elliptic partial differential equations on a perforated domain. The main results of this paper establish a link between the solution of an inverse problem on a perforated domain and ...
Herb E. Kunze, Davide La Torre
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Application of the inverse Laplace transform techniques to solve the generalized Bagley–Torvik equation including Caputo’s fractional derivative

Partial Differential Equations in Applied Mathematics
This article employs the Laplace transform approach to solve the Bagley–Torvik equation including Caputo’s fractional derivative. Laplace transform is a powerful method for enabling solving integer and non-integer order ODEs and PDEs in engineering and ...
Dania Santina, Kamran, Muhammad Asif, Salma Aljawi, Nabil Mlaiki   +4 more
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Numerical differentiation of fractional order derivatives based on inverse source problems of hyperbolic equations

Mathematical Modelling and Analysis
In this paper, we mainly study the numerical differentiation problem of computing the fractional order derivatives from noise data of a single variable function.
Zewen Wang, Shufang Qiu, Xiuxing Rui, Wen Zhang   +3 more
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An Adaptive Sampling Algorithm with Dynamic Iterative Probability Adjustment Incorporating Positional Information

Entropy
Physics-informed neural networks (PINNs) have garnered widespread use for solving a variety of complex partial differential equations (PDEs). Nevertheless, when addressing certain specific problem types, traditional sampling algorithms still reveal ...
Yanbing Liu, Liping Chen, Yu Chen, Jianwan Ding   +3 more
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Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning

Applied Sciences
Physics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems.
Abdul Hannan Mustajab, Hao Lyu, Zarghaam Rizvi, Frank Wuttke   +3 more
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